I am working with a cusp catastrophe mathematical surface; Voronoi and brick textures, apply successfully to it but not image textures. I can project an image onto an object with an image texture but when the same image is projected on the similar size cusp surface, the projection is diffused, has no detail. See image and Blender file.
What treatment/action might the cusp surface need to correctly display a projected image/video texture? I have tried unwrapping the cusp surface but didn't see any change. Does the projected image have to be rectilinear?
The cusp surface I am working was derived from a .stl print file. In case that is causing the problem, I will also attach the initial conversion. 
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$\begingroup$ <img src="https://blend-exchange.com/embedImage.png?bid=73syv0K8" /> <img src="https://blend-exchange.com/embedImage.png?bid=ZRqzGjJ1" /> $\endgroup$– Denis PostleJan 28 at 7:50
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$\begingroup$ Do you want the texture as if projected from one direction, or as if folded along with the surface? $\endgroup$– Robin Betts ♦Jan 28 at 9:48
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$\begingroup$ for some reason the image and files I posted haven't appeared, However I have progressed the problem by succeeding in (a problematic) unwrapping of the cusp surface. I'll come that in another post $\endgroup$– Denis PostleJan 29 at 10:29
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$\begingroup$ yes I want the image to be projected from above and not wrapped around underneath the cusp but I guess to do anything it needs an unwrapped object, see above $\endgroup$– Denis PostleJan 29 at 10:33
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